Traditional space deformation algorithms assume that an embedded object should be treated as a single component. However, many 3D models consist of multiple components. Problems manipulating the multiple components include time and expense for an animator to set up the joint constraints for the animation.
Constituent components of a 3D model are commonly connected by a joint of either mechanical or biological origin. These joints serve not only to segment the complex model into components, but also to constrain the relative spatial configurations of neighboring components. The deformation of different components may be represented independently of each other, which serves to eliminate the unnatural coupling that otherwise exists when multiple objects inhabit a shared space-based deformation. In addition, joints define natural degrees of freedom afforded by geometry, which allows for natural and physically-plausible deformations and poses. However, model deformation may be problematic when the model framework supports arbitrary mixes of rigid and deformable components, connected by a variety of joint types. Therefore, there is a need for a deformation framework that supports the deformation of a model including an arbitrary mix of rigid components and deformable components.